Thesis (Ph. D. in Civil Engineering)--Vanderbilt University, May 2007. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 119-124).

Elliptic partial differential equations that are used to model physical phenomena give rise to large sparse linear systems. Such systems can be symmetric positive definite and can be solved by the preconditioned conjugate gradients method. In this thesis, we develop support graph preconditioners for symmetric positive definite matrices that arise from the finite element discretization of elliptic partial differential equations. An object oriented code is developed for the construction, integration and application of these preconditioners. Experimental results show that the advantages of support graph preconditioners are retained in the proposed extension to the finite element matrices.

The solution of the secondary coupled-vector potential formulation of Maxwell??s equations governing the controlled-source electromagnetic (CSEM) response of an arbitrary, threedimensionalconductivitymodelmust be calculatednumerically.The finite elementmethod is attractive, because it allows the model to be discretized into an unstructured mesh, permitting the specification of realistic irregular conductor geometries, and permitting the mesh to be refined locally, where finer resolution is needed. The calculated results for a series ofsimple test problems, ranging from one-dimensionalscalar differentialequations to three-dimensional coupled vector equations match the known analytic solutions well, with error values several orders of magnitude smaller than the calculated values. The electromagnetic fields of a fully three-dimensional CSEM model, recovered from the potentials using the moving least squares interpolation numerical differentiation algorithm, compares well with published numerical modeling results, particularly when local refinement is applied. Multiple buried conductors in a conductive host interact via mutual induction and current flow through the host due to the dissipation of charge accumulated on the conductor boundary. The effect of this interaction varies with host conductivity, transmitter frequency, and conductor geometry, orientation, and conductivity. For three test models containingtwo highly conductive plate-like targets, oriented in various geometries (parallel, perpendicular, and horizontal), mutual coupling ranges as high as twenty times the total magnetic field. The effect of varying host conductivity is significant, especially at high frequencies. Numerical modeling also shows that the vorticity of the currents density induced in a vertically oriented plate-like conductor rotates from vertical at high frequencies, to horizontal at low frequencies, a phenomenon confirmed by comparison with time domain field data collected in Brazos County, Texas. Furthermore, the effect of the presence of a simple horst on the CSEM response of a homogeneous conductive earth is significant, even when the height of the horst is only a fraction of the skin depth of the model. When the transmitter is placedon topofthe horst, the currents inducedtherein account for nearly all of the total magnetic field of the model, indicating that topography, like mutual coupling must be accounted for when interpreting CSEM data.

The present study aims to determine the optimum blank shape design for the deep drawing of arbitrary shaped cups with a uniform trimming allowance at the flange i.e. cups without ears. This earing defect is caused by planar anisotropy in the sheet and the friction between the blank and punch/die. In this research, a new method for optimum blank shape design using finite element analysis has been proposed. Explicit non-linear finite element (FE) code LSDYNA is used to simulate the deep drawing process. FE models are constructed incorporating the exact physical conditions of the process such as tooling design like die profile radius, punch corner radius, etc., material used, coefficient of friction, punch speed and blank holder force. The material used for the analysis is mild steel. A quantitative error metric called shape error is defined to measure the amount of earing and to compare the deformed shape and target shape set for each stage of the analysis. This error metric is then used to decide whether the blank needs to be modified or not. The cycle is repeated until the converged results are achieved. This iterative design process leads to optimal blank shape. In order to verify the proposed method, examples of square cup and cylindrical cup have been investigated. In every case converged results are achieved after a few iterations. So through the investigation the proposed systematic method of optimal blank design is found to be very effective in the deep drawing process and can be further applied to other stamping applications.

Spontaneous imbibition plays a very important role in the displacement mechanism of non-wetting fluid in naturally fractured reservoirs. We developed a new 2D two-phase finite element numerical model, as available commercial simulators cannot be used to model small-scale experiments with different boundary conditions as well as complex boundary conditions such as fractures and vugs. Starting with the basic equation of fluid flow, we derived the non-linear diffusion saturation equation. This equation cannot be put in weighted-integral weak variational form and hence Rayleigh-Ritz finite element method (FEM) cannot be applied. Traditionally, the way around it is to use higher order interpolation functions and use Galerkin FEM or reduce the differentiability requirement and use Mixed FEM formulation. Other FEM methods can also be used, but iterative nature of those methods makes them unsuitable for solving large-scale field problems. But if we truncate the non-linear terms and decouple the dependent variables, from the spatial as well as the temporal domains of the primary variable to solve them analytically, the non-linear FEM problem reduces to a simple weighted integral form, which can be put into its corresponding weak form. The advantage of using Rayleigh-Ritz method is that it has immediate effect on the computation time required to solve a particular problem apart from incorporating complex boundary conditions. We compared our numerical models with the analytical solution of this diffusion equation. We validated the FDM numerical model using X-Ray Tomography (CT) experimental data from the single-phase spontaneous imbibition experiment, where two simultaneously varying parameters of weight gain and CT water saturation were used and then went ahead and compared the results of FEM model to that of FDM model. A two-phase field size example was taken and results from a commercial simulator were compared to the FEM model to bring out the limitations of this approach.

Modeling of single-walled carbon nanotubes, multi-walled nanotubes and nanotube reinforced polymer composites using both the Finite Element method and the Molecular Dynamic simulation technique is presented. Nanotubes subjected to mechanical loading have been analyzed. Elastic moduli and thermal coefficient of expansion are calculated and their variation with diameter and length is investigated. In particular, the nanotubes are modeled using 3D elastic beam finite elements with six degrees of freedom at each node. The difficulty in modeling multi walled nanotubes is the van der Waal's forces between adjacent layers which are geometrically non linear in nature. These forces are modeled using truss elements. The nanotube-polymer interface in a nano-composite is modeled on a similar basis. While performing the molecular dynamic simulations, the geometric optimization is performed initially to obtain the minimized configuration and then the desired temperature is attained by rescaling the velocities of carbon atoms in the nanotube. Results show that the Young's modulus increases with tube diameter in molecular mechanics whereas decreases in molecular dynamics since the inter-atomic potential due to chemical reactions between the atoms is taken into consideration in molecular dynamics unlike in molecular mechanics.

As technological advances occur, many conventional materials are incapable of providing the unique multi-functional characteristics demanded thus driving an accelerated focus to create new material systems such as carbon and graphite foams. The improvement of their mechanical stiffness and strength, and tailoring of thermal and electrical conductivities are two areas of multi-functionality with active interest and investment by researchers. The present research focuses on developing models to facilitate and assess multi-functional carbon foams in an effort to expand knowledge. The foundation of the models relies on a unique approach to finite element meshing which captures the morphology of carbon foams. The developed models also include ligament anisotropy and coatings to provide comprehensive information to guide processing researchers in their pursuit of tailorable performance. Several illustrations are undertaken at multiple scales to explore the response of multi-functional carbon foams under coupled field environments providing valuable insight for design engineers in emerging technologies. The illustrations highlight the importance of individual moduli in the anisotropic stiffness matrix as well as the impact of common processing defects when tailoring the bulk stiffness. Furthermore, complete coating coverage and quality interface conditions are critical when utilizing copper to improve thermal and electrical conductivity of carbon foams.

In the past two decades depth-sensing indentation has becomea widely used technique to measure the mechanical properties ofmaterials. This technique is particularly suitable for thecharacterisation of materials at sub-micro or nano scale thoughthere is a tendency to extend its application to the micro ormacro scale. The load-penetration depth curve of depth-sensingindentation is a characteristic of a material and can be usedfor analysing various mechanical properties in addition tohardness. This thesis deals with the mechanicalcharacterisation of bulk materials, thin films and coatings,gradient materials, and composites using depth-sensingindentation. Finite element method has been resorted to as atool to understand the indentation behaviour of materials. The piling-up or sinking-in behaviour of materials plays animportant role in the accurate determination of materialsproperties using depth-sensing indentation. Finite elementsimulations show that the piling-up or sinking-in behaviour isdetermined by the material parameters, namelyE/σyratio and strain hardening exponent orexperimental parameterhe/hmaxratio, and the contact friction. Anempirical model has been proposed to relate the contact area ofindentation to theE/σyratio and thehe/hmaxratio and used to predict thepiling-up orsinking-in of materials. The existence of friction is found toenhance the sinking-in tendency of materials. A generalrelationship between the hardness and the indentationrepresentative stress valid for both soft and hard materialshas been obtained. A possible method to estimate the plasticproperties of bulk materials has been suggested. Measuring the coating-only properties requires theindentation to be done within a critical penetration depthbeyond which substrate effect comes in. The ratio of thecritical penetration depth to the coating thickness determinedby nanoindentation is independent of coating thickness andabout 0.2 for gold / nickel, 0.4 for aluminium / BK7 glass, and0.2 for diamond-like-carbon / M2 steel and alumina / nickel.Finite element simulations show that this ratio is dependent onthe combination of the coating and the substrate and moresensitive to differences in the elastic properties than in theplastic properties of the coating/substrate system. Thedeformation behaviour of coatings, such as, piling-up of thesoft coatings and cracking of the hard coatings, has also beeninvestigated using atomic force microscope. The constraint factors, 2.24 for WC phase and 2.7 for WC-Cocemented carbides, are determined through nanoindentation andfinite element simulations. A modified hardness model of WC-Cocemented carbides has been proposed, which gives a betterestimation than the Lee and Gurland hardness model. Finiteelement method has also been used to investigate theindentation behaviour of WC-Co gradient coatings. Keywords:depth-sensing indentation, nanoindentation,finite element method, atomic force microscope, mechanicalproperties, hardness, deformation, dislocations, cracks,piling-up, sinking-in, indentation size effect, thin coatings,composite, gradient materials, WC-Co, diamond-like-carbon,alumina, gold, aluminium, nickel, BK7 glass, M2 steel.

Injuries to the neck, or cervical region, are very importantsince there is a potential risk of damage to the spinal cord.Any neck injury can have devastating if not life threateningconsequences. High-speed transportation as well as leisure-timeadventures have increased the number of serious neck injuriesand made us increasingly aware of its consequences.Surveillance systems and epidemiological studies are importantprerequisites in defining the scope of the problem. Thedevelopment of mechanical and clinical tools is important forprimary prevention of neck injuries. Thus, the main objectives of the present doctoral thesisare:- To illustrate the dimension of cervical injuries inSweden,- To develop a Finite Element (FE) model of the uppercervical spine, and- To study spinal stability for cervical injuries. The incidence studies were undertaken with data from theinjury surveillance program at the Swedish National Board ofHealth and Welfare. All in-patient data from Swedish hospitals,ranging over thirteen years from 1987 to 1999, were analyzed.During this period 14,310 nonfatal and 782 fatal cervicalinjuries occurred. The lower cervical spine is the mostfrequent location for spinal trauma, although, this changeswith age so that the upper cervical spine is the most frequentlocation for the population over 65 years of age. The incidencefor cervical fractures for the Swedish population decreased forall age groups, except for those older than 65 years of age.The male population, in all age groups, has a higher incidencefor neck fractures than females. Transportation relatedcervical fractures have dropped since 1991, leaving fallaccidents as the sole largest cause of cervical trauma. An anatomically detailed FE model of the human uppercervical spine was developed. The model was validated to ensurerealistic motions of the joints, with significant correlationfor flexion, extension, lateral bending, axial rotation, andtension. It was shown that an FE-model could simulate thecomplex anatomy and mechanism of the upper cervical spine withgood correlation to experimental data. Three studies wereconducted with the FE model. Firstly, the model of the uppercervical spine was combined with an FE model of the lowercervical spine and a head model. The complete model was used toinvestigate a new car roof structure. Secondly, the FE modelwas used for a parameter study of the ligament materialcharacteristics. The kinematics of the upper cervical spine iscontrolled by the ligamentous structures. The ligaments have tomaintain spinal stability while enabling for large rotations ofthe joints. Thirdly, the FE-model was used to study spinalinjuries and their effect on cervical spinal stability inflexion, extension, and lateral bending. To do this, the intactupper cervical spine FE model was modified to implementruptures of the various spinal ligaments. Transection of theposterior atlantooccipital membrane, the ligametum flavum andthe capsular ligament had the most impact on flexion, while theanterior longitudinal ligament and the apical ligamentinfluenced extension. It is concluded that neck injuries in Sweden is a problemthat needs to be address with new preventive strategies. It isespecially important that results from the research on fallaccidents among the elderly are implemented in preventiveprograms. Secondly, it is concluded that an FE model of thecervical region is a powerful tool for development andevaluation of preventive systems. Such models will be importantin defining preventive strategies for the future. Lastly, it isconcluded that the FE model of the cervical spine can increasethe biomechanical understanding of the spine and contribute inanalyses of spinal stability.